0.1 Import Data

if (!require("pacman")) install.packages("pacman")
pacman::p_load(tidyverse, broom, skimr, devtools, ggpubr, mgcv, extrafont, mgcViz, here)

theme_set(theme_pubclean(base_size = 14))

# load the function to print GAM figures
source(here("R", "p_gam.R"))
# import
lesion <- read_csv(here("cache", "summarised_lesion_data.csv"))
weather <- read_csv(here("cache", "weather_summary.csv"))

dat <- left_join(lesion, weather, by = c("site" = "Location", "rep" = "Rep"))

0.2 Fit GAMs

For reproducibility purposes, use set.seed().

set.seed(27)

0.2.1 mod1 - s(Distance)

mod1 <-
   gam(
      mean_pot_count ~ s(distance, k = 5),
      data = dat
   )

summary(mod1)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## mean_pot_count ~ s(distance, k = 5)
## 
## Parametric coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept)   1.0802     0.0475    22.7 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##              edf Ref.df    F             p-value    
## s(distance) 3.93      4 78.4 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.482   Deviance explained = 48.8%
## GCV = 0.76522  Scale est. = 0.75394   n = 334
print(p_gam(x = getViz(mod1)) +
         ggtitle("s(Distance)"),
      pages = 1)

0.2.2 mod2 - s(Distance) + Precipitation

mod2 <-
   gam(
      mean_pot_count ~ sum_rain+ s(distance, k = 5),
      data = dat
   )

summary(mod2)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## mean_pot_count ~ sum_rain + s(distance, k = 5)
## 
## Parametric coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept)  1.11372    0.05794   19.22 <0.0000000000000002 ***
## sum_rain    -0.00740    0.00733   -1.01                0.31    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##              edf Ref.df    F             p-value    
## s(distance) 3.93      4 78.4 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.482   Deviance explained = 48.9%
## GCV = 0.76751  Scale est. = 0.75389   n = 334
print(p_gam(x = getViz(mod2)) +
         ggtitle("s(Distance) + Precipitation"),
      pages = 1)

0.2.3 mod3 - s(Distance) + Windspeed

mod3 <-
   gam(mean_pot_count ~ mws + s(distance, k = 5),
       data = dat)

summary(mod3)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## mean_pot_count ~ mws + s(distance, k = 5)
## 
## Parametric coefficients:
##             Estimate Std. Error t value     Pr(>|t|)    
## (Intercept)   0.6855     0.1093    6.27 0.0000000011 ***
## mws           0.1213     0.0304    3.99 0.0000823409 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##              edf Ref.df    F             p-value    
## s(distance) 3.93      4 81.9 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.504   Deviance explained = 51.1%
## GCV = 0.7343  Scale est. = 0.72127   n = 334
print(p_gam(x = getViz(mod3)) +
         ggtitle("s(Distance) + Windspeed"),
      pages = 1)

0.2.4 mod4 - s(Distance) + Windspeed + Precipitation

mod4 <-
   gam(mean_pot_count ~ sum_rain + mws + s(distance, k = 5),
       data = dat)

summary(mod4)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## mean_pot_count ~ sum_rain + mws + s(distance, k = 5)
## 
## Parametric coefficients:
##             Estimate Std. Error t value      Pr(>|t|)    
## (Intercept)  0.71328    0.11019    6.47 0.00000000035 ***
## sum_rain    -0.01255    0.00725   -1.73         0.085 .  
## mws          0.13019    0.03076    4.23 0.00003000169 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##              edf Ref.df    F             p-value    
## s(distance) 3.93      4 82.4 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.507   Deviance explained = 51.6%
## GCV = 0.7321  Scale est. = 0.71691   n = 334
print(p_gam(x = getViz(mod4)) +
         ggtitle("s(Distance) + Windspeed + Precipitation"),
      pages = 1)

0.2.5 mod5 - s(Distance + Windspeed) + Precipitation

mod5 <-
   gam(
      mean_pot_count ~ sum_rain + s(distance + mws, k = 5),
      data = dat
   )
## Warning in term[i] <- attr(terms(reformulate(term[i])), "term.labels"): number
## of items to replace is not a multiple of replacement length
summary(mod5)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## mean_pot_count ~ sum_rain + s(distance + mws, k = 5)
## 
## Parametric coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept)  1.11372    0.05794   19.22 <0.0000000000000002 ***
## sum_rain    -0.00740    0.00733   -1.01                0.31    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##              edf Ref.df    F             p-value    
## s(distance) 3.93      4 78.4 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.482   Deviance explained = 48.9%
## GCV = 0.76751  Scale est. = 0.75389   n = 334
print(p_gam(x = getViz(mod5)) +
         ggtitle("s(Distance + Windspeed) + Precipitation"),
      pages = 1)

0.2.6 mod6 - s(Distance) + s(Windspeed) + Precipitation

mod6 <-
   gam(
      mean_pot_count ~ sum_rain + s(distance, k = 5) + s(mws, k = 5),
      data = dat
   )

summary(mod6)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## mean_pot_count ~ sum_rain + s(distance, k = 5) + s(mws, k = 5)
## 
## Parametric coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)   0.5192     0.2687    1.93    0.054 .
## sum_rain      0.1241     0.0586    2.12    0.035 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##              edf Ref.df    F              p-value    
## s(distance) 3.94   4.00 93.8 < 0.0000000000000002 ***
## s(mws)      3.83   3.97 17.2      0.0000000000014 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.566   Deviance explained = 57.8%
## GCV = 0.6495  Scale est. = 0.63051   n = 334
print(p_gam(x = getViz(mod6)) +
         ggtitle("s(Distance) + s(Windspeed) + Precipitation"),
      pages = 1)

0.2.7 mod7 - s(Distance) + s(Windspeed)

mod7 <-
   gam(
      mean_pot_count ~ s(distance, k = 5) + s(mws, k = 5),
      data = dat
   )

summary(mod7)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## mean_pot_count ~ s(distance, k = 5) + s(mws, k = 5)
## 
## Parametric coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept)   1.0802     0.0437    24.7 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##              edf Ref.df    F              p-value    
## s(distance) 3.94   4.00 92.6 < 0.0000000000000002 ***
## s(mws)      3.27   3.62 16.2       0.000000000033 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.561   Deviance explained =   57%
## GCV = 0.65512  Scale est. = 0.63903   n = 334
print(p_gam(x = getViz(mod7)) +
         ggtitle("s(Distance) + s(Windspeed)"),
      pages = 1)

0.2.8 mod8 - s(Distance) + s(Windspeed) + s(Precipitation)

mod8 <-
   gam(
      mean_pot_count ~ s(distance, k = 5) + s(mws, k = 5) + s(sum_rain, k = 5),
      data = dat
   )

summary(mod8)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## mean_pot_count ~ s(distance, k = 5) + s(mws, k = 5) + s(sum_rain, 
##     k = 5)
## 
## Parametric coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept)   1.0802     0.0434    24.9 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##              edf Ref.df     F              p-value    
## s(distance) 3.94   4.00 93.81 < 0.0000000000000002 ***
## s(mws)      3.83   3.97 17.18      0.0000000000014 ***
## s(sum_rain) 1.00   1.00  4.47                0.035 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.566   Deviance explained = 57.8%
## GCV = 0.6495  Scale est. = 0.63051   n = 334
print(p_gam(x = getViz(mod8)) +
         ggtitle("s(Distance) + s(Windspeed) + s(Precipitation)"),
      pages = 1)

0.2.9 mod9 - s(Distance) + s(Precipitation)

mod9 <-
   gam(
      mean_pot_count ~ s(distance, k = 5) + s(sum_rain, k = 5),
      data = dat
   )

summary(mod9)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## mean_pot_count ~ s(distance, k = 5) + s(sum_rain, k = 5)
## 
## Parametric coefficients:
##             Estimate Std. Error t value            Pr(>|t|)    
## (Intercept)   1.0802     0.0434    24.9 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##              edf Ref.df    F              p-value    
## s(distance) 3.94      4 94.1 < 0.0000000000000002 ***
## s(sum_rain) 3.95      4 17.6     0.00000000000092 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.568   Deviance explained = 57.8%
## GCV = 0.64583  Scale est. = 0.62864   n = 334
print(p_gam(x = getViz(mod9)) +
         ggtitle("s(Distance) + s(Precipitation)"),
      pages = 1)

0.2.10 mod10 - s(Distance) +s(Precipitation) + Windspeed

mod10 <-
   gam(
      mean_pot_count ~ s(distance, k = 5) + s(sum_rain, k = 5) + mws,
      data = dat
   )

summary(mod10)
## 
## Family: gaussian 
## Link function: identity 
## 
## Formula:
## mean_pot_count ~ s(distance, k = 5) + s(sum_rain, k = 5) + mws
## 
## Parametric coefficients:
##             Estimate Std. Error t value           Pr(>|t|)    
## (Intercept)  1.04950    0.12494    8.40 0.0000000000000014 ***
## mws          0.00945    0.03599    0.26               0.79    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##              edf Ref.df    F              p-value    
## s(distance) 3.94      4 93.8 < 0.0000000000000002 ***
## s(sum_rain) 3.95      4 12.7         0.0000000016 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.566   Deviance explained = 57.8%
## GCV = 0.64973  Scale est. = 0.63051   n = 334
print(p_gam(x = getViz(mod10)) +
         ggtitle("s(Distance) + s(Precipitation) + Windspeed"),
      pages = 1)

0.2.11 mod11.0 - s(Distance) + s(Windspeed) + s(Precipitation), family = tw()

This is the same as mod8 but using family = tw(), see ?family.mgcv for more on the families. The Tweedie distribution is used where the distribution has a positive mass at zero, but is continuous unlike the Poisson distribution that requires count data. The data visualisation shows clearly that the mean pot count data have this shape.

mod11.0 <-
   gam(
      mean_pot_count ~ s(distance, k = 5) + 
         s(mws, k = 5) + 
         s(sum_rain, k = 5),
      data = dat,
      family = tw()
   )

summary(mod11.0)
## 
## Family: Tweedie(p=1.044) 
## Link function: log 
## 
## Formula:
## mean_pot_count ~ s(distance, k = 5) + s(mws, k = 5) + s(sum_rain, 
##     k = 5)
## 
## Parametric coefficients:
##             Estimate Std. Error t value    Pr(>|t|)    
## (Intercept)   -0.228      0.041   -5.57 0.000000053 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##              edf Ref.df      F              p-value    
## s(distance) 3.50   3.85 123.78 < 0.0000000000000002 ***
## s(mws)      1.98   2.01  10.23             0.000037 ***
## s(sum_rain) 2.86   2.97   4.48                0.003 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.674   Deviance explained = 61.2%
## -REML = 309.53  Scale est. = 0.36395   n = 334
print(p_gam(x = getViz(mod11.0)) +
   ggtitle("s(Distance) + s(Windspeed) + s(Precipitation), family = tw()"),
   pages = 1)

0.2.12 mod11.1 - s(Distance, bs = “ts”) + s(Windspeed, bs = “ts”) + s(Precipitation, bs = “ts”), family = tw()

mod11.1 <-
   gam(
      mean_pot_count ~ s(distance, k = 5, bs = "ts") + 
         s(mws, k = 5, bs = "ts") + 
         s(sum_rain, k = 5, bs = "ts"),
      data = dat,
      family = tw()
   )

summary(mod11.1)
## 
## Family: Tweedie(p=1.044) 
## Link function: log 
## 
## Formula:
## mean_pot_count ~ s(distance, k = 5, bs = "ts") + s(mws, k = 5, 
##     bs = "ts") + s(sum_rain, k = 5, bs = "ts")
## 
## Parametric coefficients:
##             Estimate Std. Error t value    Pr(>|t|)    
## (Intercept)  -0.2239     0.0409   -5.47 0.000000088 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Approximate significance of smooth terms:
##                  edf Ref.df     F             p-value    
## s(distance) 3.248778      4 117.8 <0.0000000000000002 ***
## s(mws)      3.354524      4  23.3 <0.0000000000000002 ***
## s(sum_rain) 0.000176      4   0.0                0.57    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## R-sq.(adj) =  0.663   Deviance explained = 60.4%
## -REML = 315.48  Scale est. = 0.36466   n = 334
print(
   p_gam(x = getViz(mod11.1)) +
      ggtitle(
         "s(Distance, bs = 'ts') + s(Windspeed, bs = 'ts')\n+ s(Precipitation, bs = 'ts'), family = tw()"
      ),
   pages = 1
)

This model, same structure as mod11.0, uses thin-plate splines to shrink the coefficients of the smooth to zero when possible.

0.3 Compare the Models

0.3.1 AIC, BIC

models <- list(mod1 = mod1,
               mod2 = mod2,
               mod3 = mod3,
               mod4 = mod4,
               mod5 = mod5,
               mod6 = mod6,
               mod7 = mod7,
               mod8 = mod8,
               mod9 = mod9,
               mod10 = mod10,
               mod11.0 = mod11.0,
               mod11.1 = mod11.1
               )
map_df(models, glance, .id = "model") %>%
   arrange(AIC)
## # A tibble: 12 x 7
##    model      df logLik   AIC   BIC deviance df.residual
##    <chr>   <dbl>  <dbl> <dbl> <dbl>    <dbl>       <dbl>
##  1 mod11.0  9.34  -320.  663.  708.     140.        325.
##  2 mod11.1  7.60  -330.  681.  720.     144.        326.
##  3 mod9     8.89  -392.  804.  841.     204.        325.
##  4 mod6     9.77  -392.  805.  846.     204.        324.
##  5 mod8     9.76  -392.  805.  846.     204.        324.
##  6 mod10    9.88  -392.  806.  847.     204.        324.
##  7 mod7     8.20  -395.  808.  843.     208.        326.
##  8 mod4     6.93  -415.  846.  876.     234.        327.
##  9 mod3     5.93  -416.  847.  873.     237.        328.
## 10 mod1     4.93  -424.  860.  883.     248.        329.
## 11 mod2     5.93  -424.  861.  888.     247.        328.
## 12 mod5     5.93  -424.  861.  888.     247.        328.

0.3.2 R2

enframe(c(
   mod1 = summary(mod1)$r.sq,
   mod2 = summary(mod2)$r.sq,
   mod3 = summary(mod3)$r.sq,
   mod4 = summary(mod4)$r.sq,
   mod5 = summary(mod5)$r.sq,
   mod6 = summary(mod6)$r.sq,
   mod7 = summary(mod7)$r.sq,
   mod8 = summary(mod8)$r.sq,
   mod9 = summary(mod9)$r.sq,
   mod10 = summary(mod10)$r.sq,
   mod11.0 = summary(mod11.0)$r.sq,
   mod11.1 = summary(mod11.1)$r.sq
)) %>%
   arrange(desc(value))
## # A tibble: 12 x 2
##    name    value
##    <chr>   <dbl>
##  1 mod11.0 0.674
##  2 mod11.1 0.663
##  3 mod9    0.568
##  4 mod10   0.566
##  5 mod6    0.566
##  6 mod8    0.566
##  7 mod7    0.561
##  8 mod4    0.507
##  9 mod3    0.504
## 10 mod2    0.482
## 11 mod5    0.482
## 12 mod1    0.482

0.3.3 ANOVA

anova(mod1,
      mod2,
      mod3,
      mod4,
      mod5,
      mod6,
      mod7,
      mod8,
      mod9,
      mod10,
      mod11.0,
      mod11.1,
      test = "F")
## Analysis of Deviance Table
## 
## Model  1: mean_pot_count ~ s(distance, k = 5)
## Model  2: mean_pot_count ~ sum_rain + s(distance, k = 5)
## Model  3: mean_pot_count ~ mws + s(distance, k = 5)
## Model  4: mean_pot_count ~ sum_rain + mws + s(distance, k = 5)
## Model  5: mean_pot_count ~ sum_rain + s(distance + mws, k = 5)
## Model  6: mean_pot_count ~ sum_rain + s(distance, k = 5) + s(mws, k = 5)
## Model  7: mean_pot_count ~ s(distance, k = 5) + s(mws, k = 5)
## Model  8: mean_pot_count ~ s(distance, k = 5) + s(mws, k = 5) + s(sum_rain, 
##     k = 5)
## Model  9: mean_pot_count ~ s(distance, k = 5) + s(sum_rain, k = 5)
## Model 10: mean_pot_count ~ s(distance, k = 5) + s(sum_rain, k = 5) + mws
## Model 11: mean_pot_count ~ s(distance, k = 5) + s(mws, k = 5) + s(sum_rain, 
##     k = 5)
## Model 12: mean_pot_count ~ s(distance, k = 5, bs = "ts") + s(mws, k = 5, 
##     bs = "ts") + s(sum_rain, k = 5, bs = "ts")
##    Resid. Df Resid. Dev        Df Deviance        F               Pr(>F)    
## 1        329        248                                                     
## 2        328        247  1.000008        1     2.11               0.1470    
## 3        328        237  0.000354       11 83105.02      0.0000000000095 ***
## 4        327        234  1.000059        2     5.90               0.0157 *  
## 5        328        247 -1.000413      -13    35.30      0.0000000072711 ***
## 6        324        204  3.972107       43    29.67 < 0.0000000000000002 ***
## 7        325        208 -1.347884       -4     7.66               0.0026 ** 
## 8        324        204  1.347362        4     7.66               0.0026 ** 
## 9        325        204 -0.972597        0                                  
## 10       324        204  0.999445        0     0.05               0.8218    
## 11       324        639  0.343094     -435                                  
## 12       325        660 -1.162338      -21    49.64      0.0000000000005 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

0.3.4 Check Best Model Fit

0.3.4.1 Mod11.0 - s(Distance) + s(Windspeed) + s(Precipitation), family = tw()

mod11.0_vis <- getViz(mod11.0)
check(mod11.0_vis,
      a.qq = list(method = "tnorm", 
                  a.cipoly = list(fill = "light blue")), 
      a.respoi = list(size = 0.5), 
      a.hist = list(bins = 10))
## 
## Method: REML   Optimizer: outer newton
## full convergence after 7 iterations.
## Gradient range [-0.0003024,-0.000000006342]
## (score 309.5 & scale 0.3639).
## Hessian positive definite, eigenvalue range [0.4238,2979].
## Model rank =  13 / 13 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##               k'  edf k-index p-value   
## s(distance) 4.00 3.50    0.86   0.010 **
## s(mws)      4.00 1.98    0.89   0.045 * 
## s(sum_rain) 4.00 2.86    0.89   0.040 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

0.3.4.2 Mod11.0 - s(Distance, family = “ts”) + s(Windspeed, family = “ts”) + s(Precipitation, family = “ts”), family = tw()

mod11.1_vis <- getViz(mod11.1)
check(mod11.1_vis,
      a.qq = list(method = "tnorm", 
                  a.cipoly = list(fill = "light blue")), 
      a.respoi = list(size = 0.5), 
      a.hist = list(bins = 10))
## 
## Method: REML   Optimizer: outer newton
## full convergence after 11 iterations.
## Gradient range [-0.00007463,0.00003687]
## (score 315.5 & scale 0.3647).
## Hessian positive definite, eigenvalue range [0.00007462,2980].
## Model rank =  13 / 13 
## 
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
## 
##                   k'      edf k-index p-value   
## s(distance) 4.000000 3.248778    0.84   0.005 **
## s(mws)      4.000000 3.354524    0.86   0.005 **
## s(sum_rain) 4.000000 0.000176    0.87   0.005 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

0.4 Thoughts

This model, mod11.0, mean_pot_count ~ s(Distance) + s(Windspeed) + s(Precipitation) - family = tw(), is the best performing model. It cannot be used for predictions, but suitably describes the dispersal data we have on hand with the parameters used. More data would be desireable to increase the value of k as evidenced in the GAM checks.